There exists a variety of experiments involving human subjects in which one desires to compare two populations relative to a measurement Y where Y depends on some variables X1,...,Xk, k is greater than or equal to 1 and where the value of X1 for each i cannot be controlled but yet is restricted to a finite interval. In such experiments it is not possible to erase the effect of the Xi's by randomization. One such example is where one population consists of healthy controls and the other consists of subjects which have some disease. Thus, the main objective of this research is to develop procedures for comparing two or more populations relative to a measurement Y where Y depends on the variables X1,...Xk, k is greater than or equal to 1. These comparisons will be formulated in a hypothesis testing framework. Both parametric and distribution-free solutions will be sought. The basic approach in both the parametric and distribution-free solutions will be to use regression techniques to find a suitable relationship between Y and X1,...,Xk and then make use of this relationship in constructing a test for the particular hypothesis of interest. It will probably be necessary to use numerical integration as well as monte carlo techniques in order to investigate properties of these tests.